'Write that down for me." The customs official slides a coffee-marked napkin over the counter. It is late afternoon, I am in Los Angeles airport, and the woman in the crisp, blue uniform wants to know precisely which band I have flown here to interview. In blue Biro, I print the words: The Ting Tings. "Ting Tings," she reads aloud, and frowns. "Huh. Yeah. I think I heard o' them."

The Ting Tings, Katie White and Jules De Martino, are a duo from Salford who are now fast gathering recognition in America, thanks largely to their appearance in the latest iPod commercial, a spot that did much to bolster the careers of Jet, CSS and Feist. Back in the UK, they have already enjoyed that first bright burst of success thanks to a number one single, That's Not My Name, that knocked Madonna off the top spot, and a number one album, We Started Nothing. Theirs is an infectious strain of shouty pop - Toni Basil meets Talking Heads - that carries easily from Topshop changing room to dance floor to festival marquee, and has already positioned itself to be the defining sound of 2008.

When the band take to the stage a couple of hours later at LA's famous Troubadour, the response is tremendous: clapping and whooping, with grown women punching the air, the audience appearing disarmingly familiar with all the lyrics. Behind the drums, De Martino sits wearing a pair of dark glasses, his face impassive as White goes scudding across the stage, kicking and shouting and beating the bass drum, all layered clothes and bleached blond hair. For all the comparisons to Debbie Harry and Wendy James, the person White most resembles at this moment is the girl who dances alone at the disco, lost entirely in the music. It is an exhilarating performance, and afterwards the dressing room is crowded with well-wishers and habitués - label bosses, local DJs, Har Mar Superstar, Drew Barrymore.

The next day, White and De Martino are playing table tennis in Beverly Hills. He in a fluoro T-shirt, red Ray-Bans and green trainers, she in black leggings, beige dress and blue sailor jacket. They are at AOL headquarters, waiting to perform a session to be broadcast online. Putt putt goes the ping-pong ball. In the background a nature programme murmurs about wolves, and White is recalling her visit to a Los Angeles throat doctor: "Thousands of gold discs on the wall!" she says. "I've never seen anything like it!" Putt putt. "People like Whitney Houston send their throat doctor their gold discs!"

In the dark of the control room, we watch through the monitors as the band play five of their songs: Great DJ, Shut Up And Let Me Go, That's Not My Name, Fruit Machine and Traffic Light. Many take a literal object - a traffic light or a fruit machine, say - turn it into an analogy for a relationship, and then stretch the metaphor to breaking point. "You keep playing me like a fruit machine," White sings in one instance, "Putting in change systematically/Winning streak that you had over me/It's turned into broken tragedy." It's a songwriting technique that stations them firmly in the primary-coloured realm of pop music.

It was a shared love of pop that brought them together - De Martino, an art school graduate and indie band member from London, and White, one third of a girl band from Lancashire, nine years his junior. They were recording in adjacent studios, both frustrated by the bands they were in, and began discussing a mutual passion for Portishead that made them wonder if they should try writing together.

"Portishead was the middle ground," De Martino says as he autographs drumheads with the Ting Tings logo. "In all the bands I'd been in before, I'd wanted to do something different, but it was only when I met Katie that I realised what. Katie knows hits when she hears them. I mean, That's Not My Name, I just didn't hear it. She can hear a hit."

"I'm a big fan of pop," White says. "I had the Take That pencil case and everything." A natural performer, she grew up singing and dancing to music she heard on the radio, listening to her parents' Motown tapes, buying Big Mountain and Alisha's Attic records, before forming a band with two schoolfriends. They played at local schools and at the St Helens Show, and on the same bill as Steps and 5ive. "But, like, 20 bands apart. Later, I heard bands like Talking Heads and Tom Tom Club, and they're still pop music, but they're creative, real pop."

After the AOL session, they shuttle to a photoshoot on a residential street. The houses are low-lying and neat, cacti sprawl across their gardens and, in the distance, the Hollywood hills rise cool and misty and blue. In the afternoon heat, White and De Martino are posing for the camera, pretending to shift a piano along the tarmac. "Do you ever get a show called the Chuckle Brothers here?" White asks, a televisual reference lost on the make-up artist powdering her brow.

"I thought it would be slightly more glamorous," White says later, speaking of the expectations she had of international pop stardom. "Not that I was in it for the glamour, but I just thought... I'm sure if I had a stylist, it would be a lot easier. But I don't, and I don't want one. We're quite DIY." Still, doing it all yourself can pall; when I bumped into White in the hotel lobby this morning, she was bemoaning the amount of laundry she had to do and the lack of travel wash in the local drugstore. "That's the thing, you know," says De Martino, "that's what we're really surprised about - getting your clothes washed is even more stressful than playing a gig."

They were sorting their laundry when they first heard they had reached number one. "We were playing Manchester that night," White says, "but we had to do a load of washing first, and the chart show were ringing us - you have to do this fake thing where they ring you during the day and you have to pretend it's the evening, and I'm a really bad actress. I was like, 'Yeah, it's good!'" She says the words limply. Still, it was an amazing day. "We played the Academy that night and the whole audience was really hyped up," White says. "I didn't want to mention being number one till we got to playing That's Not My Name, so I could thank them, but the audience kept shouting, 'You've knocked Madonna off number one!'"

It was an especially sweet moment after what had been a somewhat crushing start in the music industry: after their first meeting, the pair formed a band called Dear Eskiimo, an appealing but less striking and slightly musically confused outfit - a catchy mix of Euro-pop, indie and trip-hop, not so different from Ting Tings, but somehow it didn't click as well. Nevertheless they were signed to Mercury. But initial excitement soon gave way to frustration, as for a year the band sat on the label unloved, undeveloped and with no prospect of putting out a record before being unceremoniously dropped.

"We lost a lot of friends," De Martino says, not a little bitterly. "People from that label who'd been hanging around and drinking with us - they didn't speak to us any more. Those people just disappeared. And it was a reality check. In effect, we felt shamed by it. We said, we cannot afford for that ever to happen in our lives again." Instead, De Martino decided to produce and write for other bands. It was White who encouraged him to give pop success another shot.

"I just felt like I had something to say," she says. "I was quite happy-go-lucky until we went through what we went through with our last band. It's not the worst problem in the world, but it was our problem at the time... bailiffs knocking at the door. In some ways it was the best thing that happened to us, because it gave me a little chip on my shoulder, so I actually had something to shout about."

Specifically, one of the things White wanted to shout about was the way she was treated as a young woman in the music industry, a subject she explores in That's Not My Name, with its long list of women's names and the sweetly-sung refrain, "Are you calling me darling?" "The first marketing meeting we had with our last label, I'd gone to all the effort of making a look book of all my favourite art and photographs, just to show them what I'm about," she says, her voice somewhere between upset and royally pissed off. "And I took it in and they said, 'Oh, yeah, great...' They didn't even look at it, just pushed it to one side and asked if I was prepared to take my kit off for men's magazines. And I was like, Aaargh! There's plenty of girls who can do that, and they've got bigger boobs and better faces, and I've got no idea why they thought I might do that. I would feel terrible doing that - I could never do it in a million years. So I told them to fuck off."

By this time, White and De Martino were living together - as friends - in Islington Mill, a converted cotton mill in Salford that serves as home to nearly 50 artists' studios, a gallery and a club space that has played host to cult Manchester nights such as Club Brenda, as well as a variety of live bands such as Gossip and Le Tigre. The pair worked behind the bar, and it was here that White, the self-proclaimed "pophead" and one-time Backstreet Boys fan, began her musical education: "To see Acid Mothers Temple and the Thermals... it blew my mind. Which was good."

I ask if she has encountered any snobbery over her girl band past and lack of musical grounding. "No, no," she insists. "I mean, you play Ghostbusters anywhere and I swear to God people will dance. It's just the cool clique who are snobby. And you don't particularly want to be part of that, anyway."

This is perhaps the essence of White's - and by extension, the Ting Tings' - charm: she's cool, but she's certainly not trying to be. She possesses an unapologetic naivety, an undiluted enthusiasm that proves highly contagious, both in conversation - discussing Indian meals and handstands and making her own clothes - and also up there on the stage, stalking and strutting and rapping, before suddenly closing her eyes and groping the air as she hits a high note, like a charming X Factor hopeful.

She took a similarly gung-ho approach to playing the guitar, an instrument she had never touched until 18 months ago, yet with which she thunders around the stage each night. "I didn't particularly want to be an amazing guitarist," she says. "I just wanted to make noise. It's funny, because I'm quite extrovert on stage and normally, while I'm not the quietest person in the room, I'm not the, you know..." She lifts her hands in a show of brashness.

"I think that's because you felt free to do that in that surrounding," De Martino says. When he speaks directly to White, there is often a gentleness to his tone, and you sense that he must feel protective of his 25-year-old bandmate. "The thing about the Mill, the reason it was so influential, is that it's full of artists learning and trying things. Our last band was more studio-based. This time we rehearsed through parties and experimented with music the way artists would do." It was through such uninhibited messing around with a system of musical loops and pedals that they developed a way to create such a full sound when playing live without upping the number of band members.

They named their new band the Ting Tings after one of White's former colleagues, who told her the name meant "an old bandstand" in Mandarin. It is a name they've subsequently come to question, having learned that in Japan, where they enjoy considerable success, it means, "small, cute penis".

The Ting Tings put on their first show at the Mill, luring in the punters with free beer, and received a rapturous reception. Within a short space of time, fans began arriving via MySpace. "We started getting messages from people in Brazil," White says, "saying, 'I'm a DJ, I love your song! It took me two weeks to track it down!'"

After a few more shows at the Mill, they went on a short tour with American emo band Straylight Run. "We hadn't heard of them," she says. "We thought, great, there'll be five people there, we'll just try out our stuff. And then they were a big band, it was packed with emo kids when we went on, but in the first 30 seconds you could just feel the audience liked it. It was a really strange feeling."

White, a delicate presence in conversation, miraculously transforms on stage into someone bigger and bolder. "I think because I did ballroom dancing from being young, I feel at my most comfortable on stage. And I mean every word of it when I sing." A few years ago, she says, she would plan out her performance meticulously. "But now, just to go on stage and be yourself and not know what you're going do next, I find really exciting."

The band put out their first vinyl-only single with a friend's label, Switchflicker (a relationship that soured in the wake of their success), available only in certain outlets in Manchester, New York and Berlin. Their second, similarly limited-edition single, Fruit Machine, prompted a session of 6 Music. Meanwhile, A&Rs began appearing at the parties at the Mill, eager to sign the pair. After their previous experience, they were hesitant, fearful that a major label would force them to relinquish control of songwriting and production, their artwork and their devotion to vinyl. It took two people to convince them to sign to Sony: one-time Hacienda DJ and M People member Mike Pickering, and legendary American producer Rick Rubin, who, out of the blue, sent them an email asking how they put their songs together, which they subsequently printed and stuck on their wall at the Mill.

They met Rubin the first time they played LA. "The gig was packed," De Martino says, "and there he was - Rick Rubin. This big guy with a beard. It's so new to us, we get shy."

"And I hope we keep experiencing it like that," White adds, "because the day that it's normal, it's a shame, because it's such a rare experience to think, 'Oh my God, these film stars are dancing at our shows!'"

"Or like at the Troubadour," De Martino says, "in this tiny dressing room with Drew going, 'I love your band.' You're like..." he looks down, " 'Thank you'." It does not appear to have dawned upon either of them that in the eyes of these film star hangers-on dancing at their shows and loitering around their dressing rooms, it is the Ting Tings who are the cool kids, the ones worth knowing.

White smiles. "We go quiet. Doing the Jonathan Ross show, we just felt like, 'What are we doing here?' And, oh my God, Gwyneth Paltrow was there and she was so beautiful and luminous and healthy, she must have thought I was weird because I was staring at her, studying her. And then Robert Downey Jnr gave us his phone number..." White stops and looks wide-eyed at De Martino. "Robert Downey Jnr," she says. "We forgot - we were supposed to ring him when we got to LA."

She shuffles awkwardly in her seat. "The thing is, it's when you meet these people," she waves her hand in an arc that encompasses Downey Jnr and Barrymore, Paltrow and Rubin, and her voice grows a little awed and emotional, "and they're saying they're fans of what we do, what we did with no hope, that they're fans of what we did there in Salford, with nothing..." ·

· The Ting Tings' new single, Shut Up And Let Me Go, is released on July 21.